I was looking for integrating external content (particularly from drupal based sites), but did not succeed. Nothing worked for me.

I found this module under develpment that seems to address my needs. I may be wrong, but I guess it could allow to display a particular node from another side within the current Drupal side (avoiding the stuff around like menus...)

I downloaded and activated it, but I have no clue what to do next. No documentation nor any discussions about it.
Is is a live or dead project?

The main purpose of this is for sites that have to run .html pages and drupal side-by-side.

The module has not been updated in a long time due to one major issue I found; When the drupal site is put into offline mode the SSI results display a full drupal offline page. I do have a workaround in the works for this issue and will likely commit it soon.

As long as Drupal handles standard Server Side Include tags then yes, that should work. I'm fairly certain it does, I just can't recall at the minute.
Give it a test and see what happens. I'd be interested to know the results.